Pharmacology for Anaesthesia and Intensive Care

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6 Mathematics and pharmacokinetics

constant rather than being dependent upon the concentration of drug. This is also

known as saturation kinetics and indicates that enzyme activity is maximal, so cannot

be influenced by increasing substrate concentration. An example is the metabolism

of ethanol, which proceeds at a relatively constant rate after the ingestion of a mod-

erate amount of alcohol. This is because the rate-limiting step in its metabolism

byalcohol dehydrogenase is the presence of a co-factor for the reaction, which is

present only in small quantities.

Certain processes obey first-order kinetics at low dose, but zero-order at higher

doses. For example, the metabolism of phenytoin becomes saturable within the

upper limit of the normal range, and the pharmacokinetics of thiopental obeys zero-

order kinetics when used by infusion for prolonged periods, such as in the treatment

of status epilepticus. There are two important implications of a process obeying

zero-order kinetics within a normal dose range.

First, during zero-order kinetics a small increase in dose may cause a large increase

in plasma level. If this occurs at a level near the upper limit of the therapeutic range,

toxicity may be experienced after a modest dose increase. Checking plasma con-

centration is essential to avoid toxic levels when prescribing drugs where this is a

problem, such as occurs with phenytoin.

Second, during zero-order kinetics there is no steady-state. If the rate of drug deliv-

ery exceeds the rate of drug excretion, plasma levels will continue to rise inexorably

until ingestion stops or toxicity leads to death (Figure6.15).

B

time

concentration

Zero-order kinetics

First-order kinetics

A

Figure 6.15.Transition to non-linear (zero-order) kinetics.If an infusion is started at a

constant rate at point A, initially plasma concentration rises in a negative exponential fashion

according to first-order kinetics. At point B the elimination process is overwhelmed and the

plasma concentration continues to rise in a linear fashion, according to zero-order kinetics. This

usually occurs because hepatic enzymes become saturated and work at maximum capacity.